dominant firm pricing and fringe expansion: the case of the u.s. iron and steel industry, 1907-1930

Dominant Firm Pricing and Fringe Expansion: The Case of the U.S. Iron and Steel Industry,1907-1930Author(s): Hideki YamawakiSource: The Review of Economics and Statistics, Vol. 67, No. 3 (Aug., 1985), pp. 429-437Published by: The MIT PressStable URL: http://www.jstor.org/stable/1925971 .

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DOMINANT FIRM PRICING AND FRINGE EXPANSION: THE CASE OF THE U.S. IRON AND STEEL INDUSTRY,

1907-1930

Hideki Yamawaki*

Abstract-This paper attempts to analyze the dynamic relations between market structure and behavior, applying the dominant price umbrella model to the U.S. iron and steel industry for 1907-30. The estimated equations, using time-series data, showed that the price set by U.S. Steel was continuously influenced by fringe market share while the latter was shaped by the dominant price. The dominant price gave the competitive fringe an incentive to expand output and capacity. Invest- ment behavior of the fringe then changed the industry's structure.

I. Introduction

W rHEN the United States Steel Corporation was founded in 1901, the corporation

accounted for 65.7% of the total steel ingots and castings production and 43.2% of the total pig iron production in the U.S. iron and steel industry. During the next three decades U.S. Steel's share of steel ingots and castings production declined grad- ually, reaching 54.3% in 1910, 45.8% in 1920, and 41.2% in 1930. U.S. Steel's share in the production of finished rolled products also declined.' This declining share has been explained mainly by the "dominant price umbrella" hypothesis, which argues that the dominant firm sets its price high enough to induce fringe firms to expand their capacities and outputs.2

The dynamic limit pricing model developed by Gaskins (1971) provides a general theoretical framework for this hypothesis. His model assumes that the dominant firm sets its optimal price so as to maximize its long-run profits subject to the rate at which fringe firms expand or new entrants enter the market. The expansion rate of the fringe firms is a function of the price set by the dominant firm.

Market structure at any moment in time thereby affects behavior, and behavior has a long-run feedback effect on market structure.

This paper seeks to explain the gradual decline in U.S. Steel's market share by means of a time- series model developed within the framework of a dominant firm pricing model. The empirical justifi- cation of this general model critically hinges on the following questions:

(i) Did the fringe market share have a continuous and significant effect on the U.S. Steel pricing policy?

(ii) Was the fringe expansion sensitive to the price level set by the dominant firm?

To answer these questions, this paper constructs a model which explicitly analyzes the price determination of the dominant firm, the capacity expansion decisions of both dominant and fringe firms, and the long-run feedback effect of capacity expansion on market structure. The complete model then consists of 7 structural equations that are estimated for the years 1907-1930, for which continuous annual data are available.

II. A Model of the U.S. Iron and Steel Industry, 1907-1930

The model assumes that, during the period in question, individual firms in the competitive fringe did not recognize mutual interdependence to each other. This assumption is warranted by the fact that in 1908 Jones and Laughlin, then the second largest producer, accounted for only 4.2% of industry ingot capacity while U.S. Steel's share was 50.1 %. Bethlehem, which became the second largest firm during the 1920s, held only 0.6% of total industry capacity in 1908.3 The appropriateness of this assumption will be tested later in this section in the context of investment behavior. The model also assumes that the extent of product differentia- tion in this industry is small, so that decisions on

Received for publication June 11, 1984. Revision accepted for publication November 5, 1984.

*Intemational Institute of Management, Berlin. I am especially indebted to Richard E. Caves, Robert W.

Fogel, and A. Michael Spence for valuable comments and suggestions. I also thank Barry J. Eichengreen, Leonard W. Weiss, participants in the Industrial Organization Seminar at Harvard University as well as two anonymous referees for their comments. Any remaining errors are, of course, my own.

1 These figures are according to American Iron and Steel Institute, Annual Statistical Reports.

2 See Jones (1921), pp. 186-230; Bums (1936), pp. 77-93; Stigler (1940,1950,1965), and Worcester (1957). 3 Stigler (1950), p. 30, table 1.

[ 429 1



430 THE REVIEW OF ECONOMICS AND STATISTICS

price and capacity expansion largely determine the industry's equilibrium.

A. Price Determination

The Model: The dominant firm is assumed to face actual and potential competition from fringe firms, each too small to affect market price through its output decisions. Then the dominant firm's pricing problem is to set an optimal price given that the quantity supplied by the competitive fringe depends upon the dominant firm's price. Let the market demand function be Q = f(P), where Q is the quantity demanded and P is the product price. The supply function of the fringe is a function of the product price P, Qf = g(P), where Q is the sum of outputs of the fringe firms. Given these functions and with the market assumed always cleared in equilibrium, the demand function for the dominant firm is Qd= Q - Qf, where Qd iS the dominant firm's derived demand. The dominant firm then maximizes profits given production costs and the residual demand. Notice that the elasticity of the derived demand for the dominant firm can be decomposed into the market demand elasticity and the supply elasticity of the competitive fringe. That is,

Qf Q e= Qd

*ef +Qdem ()

where ef is the supply elasticity of the competitive fringe and em is the market demand elasticity. Then the first-order condition yields

,(em -1) + ( QfQ) (ef + 1:*M 2

where Qf/Q is the market share of the fringe and MC is the marginal cost of the dominant firm.4 Note also that Qf/Q = 1 - Qd/Q where Qd/Q is the market share of the dominant firm. Equation (2) shows that the mark-up factor of the dominant firm depends on the market demand elasticity, the supply elasticity of the fringe, and the market share of the fringe (or the dominant firm's market share). Since the partial derivative of price with respect to the fringe market share is negative, an increase in the fringe market share should reduce

the price level the dominant firm sets, other things being equal.5

The dominant firm umbrella hypothesis implies that the short-run elasticity of fringe supply will increase when either the dominant price or market demand changes so as to leave fringe firms with excess capacity, because they will attempt to expand their output up to capacity by undercut- ting the going level of dominant price.6 This argument implies a negative relation between the dominant firm's mark-up factor and any index of excess capacity in the fringe, for the supply elasticity of the fringe has a negative relation with the dominant's mark-up factor.

Then the mark-up factor for the dominant firm should be specified, assuming a multiplicative form of the function, as

X = aO (FMS) al(ICU) a2 (3)

where X is the mark-up factor of the dominant firm, FMS is the fringe market share, and ICU is the index of industry capacity utilization (to capture fluctuations of the short-run supply elasticity of the fringe). The cost minimization problem under the Cobb-Douglas production function gives the short-run marginal cost as a function of unit input costs. Expressing equation (2) as P = X MC, taking the logarithm of this, and substituting the mark-up factor (3) and the marginal cost function into it, we obtain the basic equation for estimation:

log P = A + allog FMS + a2logICU +a31og USULC + a4log USUMC + e

(4)

where USULC and USUMC are U.S. Steel's unit labor cost and unit material cost, respectively, and e is an error term.

Two additional independent variables were included in equation (4). With the supply of steel from both the United Kingdom and Germany to the world market reduced, export opportunities for the U.S. steel industry increased significantly during World War I (1914-1918) and several years after. The world steel price was extremely high during these years. Without competition from these

4See Saving (1970) and Dansby and Willig (1979) for similar derivations.

5Also dP/def < 0. 6 For a brief history of price-cutting by the fringe firms under

the basing-point system during the period in question, see Daugherty, De Chazeau, and Stratton (1937), vol. 1, pp. 538-541.



DOMINANT FIRM PRICING AND FRINGE EXPANSION 431

two major steel-exporting countries, the U.S. producers could maximize profits by raising domestic steel price to the level of world steel price.] Fur- thermore, during these years the domestic price should have increased with the domestic industry's export activities. To capture this effect, an interaction variable was introduced which has the value of the logarithm of average U.S. export share for the rolled steel products for the war years (1914-1918) and zero for the other years (WWEX- PORT).

A dummy variable was employed to allow for the existence of the famous "Gary dinners." A special committee was elected at one of these dinners in 1907 for the purpose of advising members of the industry on prices, extras and other related problems.8 To see if such informal agree- ments averted price competition and maintained the price level, GARYD was introduced. GARYD is a dummy variable which has the value of unity for 1907, 1908 and 1910 and zero otherwise.9

Statistical Results: The definitions of variables are summarized in table 1.L1 Data on steel price index (P) are obtained from various issues of Iron Age. This data series, considered the most reliable source on price during the period, is a composite price series of finished steel-the monthly average of prices of steel bars, beams, tank plates, plain wire, open-hearth rails, black pipe, and black sheets. The published data seem to reflect the behavior of price set by U.S. Steel fairly well because of the existence of the basing-point system for finished steel products for most of the period."

USULC is defined as a ratio of total annual wages and salaries to steel ingots and castings production. It does not distinguish wage payments to manufacturing employees from wage payments

to iron ore mining and transportation employees. About 70%-75% of the total labor force in U.S. Steel participated in manufacturing divisions during the period. In estimation, unit material cost is omitted from the equation partly because the appropriate data for this variable are not available. As an attempt, the market price of iron ore (MP)

TABLE 1.-VARIABLE DEFINITIONS

Variable Definition

A FTSTD Dummy variable equal to one for 1920-30 and zero otherwise.

BCA P Bethlehem Steel's ingot production capacity.

BK Bethlehem Steel's capital stock. See note 17 for construction of this variable.

CONSP BLS Consumer Price Index for all items (1920 = 100.0).

CP CP = P/ WPI. FCA P Total ingot production capacity for fringe

firms. FCS Fringe capacity share, FCS =

FCA P/TCA P. FCU Fringe capacity utilization, FCU =

FX/FCA P. FK The sum of capital stock series for Beth-

lehem, Republic, Youngstown, and Arm- co. For a detailed discussion on this variable, see note 17.

FMS Fringe's market share, FMS = FX/(FX + USX).

FX Total steel ingot production of fringe firms.

GA R YD Dummy variable equal to one for 1907-08, and 1910.

ICU Industry capacity utilization, ICU= TX/TCAP.

MP Average price of iron ore. (Index of average value per long ton, 1920 = 100.0.)

TX Total industry steel ingot production. P Composite price index of finished steel

products (1920 = 100.0). STRIKED Dummy variable equal to one for 1919. TCA P Total industry steel ingot production

capacity. TIME Time trend. USCA P Total ingot production capacity for U.S.

Steel. USCU Steel ingot production capacity utilization

of U.S. Steel, USCU = USX/USCAP. USK Capital stock of U.S. Steel. See note 17

for construction of this variable. USULC Unit labor cost of U.S. Steel. The ratio of

annual wages and salaries paid to steel ingot production.

USX Total steel ingot production of U.S. Steel. WPI BLS wholesale price index for all com-

modities (1920 = 100.0). WWEXPORT Interaction variable equal to the logarithm

of average U.S. steel industry export share of rolled steel products for 1914-18 and zero otherwise.

7U.K. average unit export price was at an extremely high level during 1915-1921 compared with the pre-war level of the export price. See Burnham and Hoskins (1943), table 94 in the appendix,,U.S. Steel exported about 75% to 100% of total U.S. steel exports for the pre-war years (Parsons and Ray (1975), p. 203).

8 Daugherty, De Chazeau, and Stratton (1937), p. 540. 9 Although the "Gary dinners" functioned formally until 1911,

there were major breakdowns of the system in 1909 and 1911. This implies that the dinners worked well for 1907, 1908 and 1910. See Schroeder (1953), p. 45; Jones (1921), pp. 223-228; and Burns (1936), pp. 78-79.

l?An appendix on data sources is available from the author upon request.

11 About 90% of the sales of plates, shapes, bars, wire products, and sheets were on a Pittsburgh-plus basis until 1921. For the basing-point price system, see Burns (1936), pp. 299-317.




was used in the price equation on the presumption that it is positively correlated with shadow value that backward integrated U.S. Steel used in its decision-making.'2 However, due to its high correlation with USULC (r = 0.81), MP was eventu- ally dropped from the equation.

The following estimation procedure is used for the entire paper: first, we estimate each equation on the assumption that the residual is first-order autoregressive; and when the estimate of the autoregressive coefficient is found to be insignificant, we re-estimate the equation assuming no serial correlation. All the equations in the paper are estimated by the two-stage least squares method (2SLS), as they contain endogenous variables on the right hand side.

The final result of the price equation is presented in table 2. All the coefficients on the independent variables have the expected signs and are statistically significant. The coefficient of FMS has a significant negative value, confirming that the pricing policy of U.S. steel was influenced by fringe market share. The equation also shows that steel price was very much affected by U.S. Steel's unit labor cost. However, the coefficient of USULC may capture to some extent the effect of material costs on steel price as the latter is omitted. The coefficient on WWEXPORT shows that the domestic price level was positively affected by the exposure to the world market only when the world steel market was in disorder and world price was at a high level.'3 The coefficient on GARYD has a significant positive value, confirming that the "Gary dinners" were effective for elevating the level of steel price.

B. Capacity Expansion

The Model: The observed decline in U.S. Steel's market share was due mainly to the rapid expansion of the ongoing fringe firms rather than the entry of new firms.'4 The compound annual rate of growth of fixed assets for the years 1907-1930, was 4.1% for U.S. Steel, 12.7% for the eight smaller

firms.'" Thus, the capacity expansion processes of both the dominant and fringe firms must be analyzed to explain the change in market structure.

The dominant firm umbrella model implies that capacity expansion of the fringe is a positive function of the price charged by the dominant firm, for each fringe firm is assumed to behave as a price- taker and maximize its profit given the price. On the other hand, the dominant firm maximizes its profits subject to the follower's reaction function, so that its choice of capacity depends on the follower's choice of capacity, which in turn depends on the price level set by the dominant firm.

Given its production function, the first-order condition for long-run profit maximization of a monopolistic firm requires that the monopolist set the value of marginal revenue times the marginal product of each input equal to its price. Since we have assumed that the dominant firm has a Cobb- Douglas production function, the condition re- duces to

aK 3 P * Qd * [(em -1) + FMS(ef + 1)]

r(em + FMS - ef)

(5)

where K* is optimal capital stock, a3 is the production function's parameter on capital stock, Qd is the dominant firm's output, em is the elasticity of market demand, ef is the elasticity of fringe supply, r is the cost of capital, and FMS is fringe market share. The partial derivative of K* with respect to FMS is positive, i.e., dK*/dFMS > 0. This condition demonstrates that the dominant firm's investment policy is constrained by fringe competition. The dominant firm maximizes its profits by restricting its production capacity when it faces a lesser degree of fringe competition.

Following the model discussed above, the desired level of capital stock for the competitive fringe (FK*) and the dominant firm (USK*) is specified respectively as

FK* = bo( CP*) bl(TX*)b2 (6)

USK* = co(CP*) cl(TX*) c2(FcCS( 1)) (3 (7)

where CP* is the expected product price in real 12 This approach was suggested by a referee. '3An equation adding export share (EXPORT) shows that

the coefficient on EXPORT for the peace years is not different from zero.

14 The National Steel Corporation was the only major steel company among those which were formed during 1920-1930. See Schroeder (1953), pp. 200-203.

15 These firms are Armco, Bethlehem, Crucible, Inland, Pitts- burgh, Republic, Sharon and Youngstown. The figures were calculated from Schroeder (1953), appendix, pp. 216-227.




TABLE 2.-A SIMULTANEOUS-EQUATION SYSTEM OF THE U.S. IRON AND STEEI INDUSTRY,

1907-1930

Structural Equationsa (1) logP = - 3.990 - 0.909 log FMS + 1.088 log USULC

(6.53) (2.00) (7.74)

+ 0.717 logICU+ 0.137 WWEXPORT+ 0.148 GARYD (4.14) (4.10) (1.50)

SEE = 0.131, DW = 1.73, DF = 18

(2) logFK= - 0.944 + 0.369 log(P/WPI)+ 0.152 logTX (1.22) (1.83) (1.75)

- 0.039 log FCU(-1) + 0.911 log FK(-1) (0.54) (31.63)

SEE= 0.091, DW = 2.11, DF = 19

(3) log USK = 2.740 - 0.029 log(P/WPI) + 0.019 log TX (6.68) (0.32) (0.61)

+ 0.770 logFCS(-1) + 0.151 logUSCU(-1) (4.65) (3.33)

+ 0.684 log USK(-1) (14.09)

SEE = 0.032, DW = 2.31, DF = 18

(4) log FX= 0.447 + 1.365 logP- 1.642 log MP (0.23) (3.71) (3.43)

+ 0.901 log FCAP(-1)- 0.114 STRIKED (5.02) (0.44)

SEE = 0.241, DW = 2.38, DF = 19

(5) logUSULC = 3.418 + 0.386 logP + 1.076 logCONSP(-1) (16.35) (3.01) (4.52)

- 0.480 logUSCU+ 0.655 logP*AFTSTD (5.72) (2.06)

+ 0.005 TIME (0.53)

SEE = 0.071, DW = 1.44, P = 0.53, DF =18

(6) log FCAP= 8.403 + 0.028 log FK+ 0.288 log FK(-1) (67.05) (0.20) (2.13)

SEE = 0.057, DW = 2.08, =0.35, DF = 21

(7) logUSCAP = 6.843 + 0.303 logUSK + 0.120 logUSK(-1) (21.30) (2.37) (1.17)

SEE =0.025, DW = 1.65, P = 0.65, DF = 21

Identities: (8) FMS = FX/TX (9) USX= TX-FX

(10) TCAP = FCAP + USCAP (11) FCS = FCA P/ TCA P (12) ICU= TX/TCAP (13) USCU = USX/USCAP (14) FCU= FX/FCAP

Note: t-values are in parentheses. aAll the equations are estimated by the two-stage least squares method (2SLS). Each equation was first estimated

assulning that the error ternm follows a tirst-order autoregressive process. When the autoregressive coeflicient was found insigniticant, the equation was then estimated assunming no serial correlation.




terms, TX* is the expected industry output, and FCS(-1) is the ratio of total fringe capacity to total industry capacity at the beginning of each year.

Although the model suggests that the desired stock depends on the cost of capital services, the statistical model omits this variable because data are not available.

Since FMS is subject to short-run fluctuations caused by short-run output behavior of the fringe firms, the appropriate variable for the statistical analysis should only reflect underlying long-run fringe penetration. Hence, we use fringe capacity share lagged once (FCS(- 1)) in the U.S. Steel investment equation to capture the effect of fringe competition.

The expected level of industry output (TX*) is included here instead of individual firm's output to allow for the effect of adjustment costs. Where adjustment costs associated with investment are not negligible, the firm should smooth its capacity decisions in order to avoid the costs of adjusting capacity rapidly. Production in the U.S. steel industry increased steadily over time while production of individual firms fluctuated widely. Thus, we expect both U.S. Steel's and the fringe's total investment to follow the smooth long-term growth path of the industry.

The effect of market growth, however, may differ in U.S. Steel and the fringe. Because U.S. Steel was large when it was established, further expansion of its capacity was apparently constrained by various factors, either managerial, financial, or an- titrust. Therefore, we expect that U.S. Steel ex- panded capacity when its production capacity had been found binding in the past years, rather than responding to expected industry growth. Parallel to this argument, we predict that the fringe re- sponded more strongly to expected growth of the market. To see these points, the fringe's capacity utilization lagged once (FCU(- 1)) and U.S. Steel's capacity utilization lagged once (USCU(- 1)) were added respectively to equations (6) and (7).

Assuming a partial adjustment process of capital stock and rational expectations on price and demand and taking logarithms of equations (6) and (7), we obtain

log FK, - log FKt - = dflogbo + dfb1logCPt + dfb2logTXt

+dfb3logFCULI - dflogFKtI + Vf,t

(8)

log USK, - log USK, -1

= duslogco + dusc1logCP, + dusc2logTX, + du5c3log FCS,-1 + dusc4log USCUL-- 1

-duslog USKt1 + vus, t (9)

where df and d are the adjustment coefficients, and v is the error term.'6 These equations for estimation postulate the geometrically declining lag weights.

Statistical Results: As members of the competitive fringe, only four companies, Bethlehem, Re- public, Youngstown, and Armco are selected because continuous capital stock series are available for these companies from their annual reports. Capital stock series for U.S. Steel and the fringe firms are constructed by starting from the bench- mark capital stock in 1906 and adding deflated gross investment to the previous year's capital stock for each subsequent year. Gross investment for year t is obtained by subtracting gross fixed assets in book value in year t - 1 from those in year t.17 Steel price in real terms (CP) is the index of steel price deflated by the general wholesale price index (P7 WPI).

Both equations (8) and (9) were first estimated by Fair's method (Fair (1970)) as they contain a lagged dependent variable. However, the estimate of the autoregressive coefficient was insignificant in both equations. The final 2SLS results are re- ported in table 2. Both the equations were in the level forms.

As expected, the price variable has a significant (at the 5% level) and robust positive'8 coefficient in the fringe investment equation while it is not significant in the U.S. Steel equation. Accordingly, the long-run elasticity of capital stock with respect

16 These equations are derived from the adjustment equation

(K,IK,-,) = (K,*/K,i)d; 0 < d < 1.

See Hickman (1965) for this type of adjustment process. 17 Formally, K, = K,t1 + 1, and I, = (K, - K,'1)/PD,,

where K is capital stock in year t, I is deflated gross investment, K' is gross fixed assets in book value, and PD is the GNP implicit price deflator. The GNP implicit price deflator was used because the implicit price deflator for non-residential producers' durable equipment is available after 1929. For 1929-1948, the GNP implicit price deflator is highly correlated with the latter (r = 0.95). Replacement investment was not taken into account here due to data deficiency. However, depreciation charges prior to WWI seldom exceeded 1% of the total fixed assets (Schroeder (1953), p. 27).

18 In the fringe equation adding a lagged price variable the current variable has a highly significant and positive coefficient while the lagged variable has a negative coefficient. However, the long-run elasticity on price is again positive.




TABLE 3.-COEFFICIENTS FOR LAGGED CAPITAL STOCKS

OF BETHLEHEM AND U.S. STEEL IN INVESTMENT

EQUATIONS FOR U.S. STEEL AND BETHLEHEM

Dependent Variable

U.S. Steel Capital Stock Bethlehem Capital Stock

Independent (USK) (BK) Variable 1907-1919 1920-1930 1907-1919 1920-1930

Bethlehem Capital Stock 0.088 0.210 -

lagged one (3.22)a (3.71)a year BK(- 1)

U.S. Steel Capital Stock - - 0.345 -0.105 lagged one (0.77) (-0.15) year USK(- 1)

Note: The coefficienrts are taken from the regression equation

logK, = a + allogCP + a21ogTX + a3logKj(- 1) + al41ogKi(-1) +f

where i is company and i * j. These are estimated by the Cochrane-Orcutt method. t-values are in parentheses. aSignificant at the 1% level (one-tailed test).

to price for the fringe has a positive value. This result gives support for the dominant price hypothesis.

Industry demand (TX) is a positive and significant influence on the fringe's investment policy, while it is not significant at all for U.S. Steel. On the other hand, capacity utilization is not significant at all for the fringe's investment, while it is positive and significant for U.S. Steel's investment decisions. These results confirm clearly that sub- stantial differences existed in investment decisions for the dominant firm and the fringe firms.

Fringe capacity share in U.S. Steel's investment equation shows a significant positive effect, confirming that the investment policy of U.S. Steel was constrained by fringe competition.

Equations (6) and (7) of table 2 link the capital stocks to the ingot production capacities. These equations are simply designed to complete the simultaneous-equation system.

So far we have assumed a priori the dominant firm model as a behavioral model for the steel industry during 1907-1930. We will test this assumption in the following. This model suggests that the dominant firm takes into account the competitive fringe's reaction when it determines its capacity, while the fringe firms do not recognize interdependence with the dominant firm. If the fringe behaves as a pure competitor so that its profit function does not register any influence of the dominant's investment decisions, its choice of capacity should not respond to the dominant's

choice of capacity. On the other hand, where both dominant and fringe firms are interdependent with each other on decisions on capacity expansion, their investment decisions should depend upon one other firm's choice of capacity.

To test these alternative hypotheses, the investment equations for U.S. Steel and Bethlehem, which became the second largest in the 1920s, are estimated for the periods 1907-19 and 1920-30,19 with the rival's capacity at the beginning of each year included.2' For the purpose of comparison, the same specification is applied to each firm. The estimated coefficients on the lagged capital stock for the potential rival appear in table 3. For both periods, Bethlehem's capital stock lagged one year shows a significant positive influence on U.S. Steel's capital stock, while lagged U.S. Steel's stock is not significant at all in Bethlehem's equations. How- ever, the coefficient on the lagged stock of Bethle- hem in the U.S. Steel equation becomes larger and the t-value becomes higher in the later period (1920-30), suggesting that U.S. Steel's recognition of Bethlehem's behavior was increasing with Beth- lehem's market share.

19 Bethlehem produced 13% of total industrv ingots and cast- ing production in 1929. Its share in 1920 was 4.8%. In the earlier period, Jones and Laughlin was the second largest firm accounting for 4.2% of industry production in 1908. Parsons and Ray (1975), table 12, p. 207.

20 See Sultan (1975), vol. II, pp. 163-189 for a similar specification applied to the U.S. electrical equipment industry.




C. Fringe Supply and Market Share

The dominant firm model suggests that, where the short-run supply curve of the competitive fringe is upward sloping, the fringe's output increases with the dominant firm's price. Profit maximization by the competitive fringe firms gives the supply function as Q = (P, W, K) where Q is output, P is the price of output, W is the vector of factor prices, K is production capacity, and dQ/dP > 0, dQldw1 < 0, dQ/dK > 0. Because the model determines U.S. Steel's output as a residual, the fringe's market share should be determined by the same factors as the fringe's output. Then our fringe supply equation for estimation becomes

log FX =1 +f2logP +f3logMP

+Jf4logFCAP(-1) +f5STRIKED + e

where FX is the fringe's output, P is the dominant price for output, MP is the average price of iron ore,2' FCAP( - 1) is the fringe's production capacity at the beginning of the year, STRIKED is the dummy variable to capture the effect of a strike in 1919,22 and e is an error term.

The 2SLS result is in table 2. All the coefficients except STRIKED are highly significant and have the expected signs, thus confirming that the price set by the dominant firm determined the fringe's short-run output.

The fringe's market share is also estimated by 2SLS. The estimated equation with FCS instead of FCAP is as follows:

log FMS = - 0.118 + 0.361 log P (1.36) (3.71)

- 0.450 log MP (3.58)

+ 0.980 log FCS(-1) (5.73)

- 0.041 STRIKED (0.65)

SEE = 0.059, DW = 2.17, DF = 19

where t-values are in parentheses. This equation again indicates that the fringe consistently re- sponded to the dominant price.

D. U.S. Steel's Unit Labor Cost

Unit labor cost was found in the last section as a significant determinant of U.S. Steel's product price. However, production workers' hourly wage, a component of unit labor cost, may depend on the ability of U.S. Steel to pay. Pugel (1980) concluded that wages increase with the excess of price over the cost of all factors of production excluding labor. Then we expect wages to be positively related to product price (P), because excess profits increase with product price, other things held constant. However, the elasticity of wage to price may depend on production workers' collective bargaining efforts. It has been argued that after the general strike of 1919, working conditions in the industry improved because of increased public concern and a change in managerial atti- tudes.23 If wages were improved through such effort, the effect of price on wage should differ between the years before and after the strike.

Another component of unit labor cost, labor productivity, is controlled by the long-run productivity trend reflecting technology and the utilization of a relatively fixed portion of the labor force.24 Then we specify U.S. Steel's unit labor cost (USULC) as

log US UL C = g0 + g1logP + g2logCONSP(-1)

+ g3 log USCU + g4TIME +g5logP*AFTSTD + e

where CONSP is consumer price index, TIME is a time trend (to represent productivity growth), AFTSTD is a dummy variable with the value of unity for 1920-30 and zero for 1907-19, and e is an error term. CONSP( - 1) is meant to capture the effects of the previous year's cost of living on wages. Capacity utilization (USCU) is assumed to be correlated with the utilization of the fixed por- tions of the labor force. The interaction variable (log P*AFTSTD) tests the 1919 strike's effect on the determination of U.S. Steel's wage.

21 The assumption here is that individual fringe firms purchase iron ore at the market price. Labor cost is omitted from the ecuation due to its high collinearity with iron ore price.

The strike resulted in almost complete paralysis of the industry in the Youngstown, Buffalo, Cleveland, and Chicago districts (Vanderblue and Crum (1927), p. 29, and appendix B).

23 See Gulick (1924), pp. 22-56 and Daugherty, De Chazeau and Stratton (1937), vol. I, pp. 186-192. U.S. Steel had cardied out a non-union policy until 1933, so that the orderly channels of collective bargaining had been closed before that year. See Vanderblue and Crum (1927), p. 32 and Brooks (1940), pp. 30-45.

24 See Eckstein and Fromm (1968) for this argument.




The 2SLS result with the correction of serial correlation is in table 2. The coefficients of all the variables except TIME are significant and have the expected signs. The significant positive sign on log P*AFTSTD gives some indirect support for the hypothesis that a larger fraction of rents accru- ing to U.S. Steel was captured by production workers after the 1919 strike.

III. The Integrated System

The integrated system consists of 7 structural equations and 7 identities; 14 endogenous variables and 7 exogenous variables (TX, MP, CONSP, GARYD, STRIKED, WWEXPORT, and TIME). Table 2 presents the estimated results of the structural equations of the system for the observation period 1907-30. In the model specification presented in table 2, fringe market share is determined by identity (8) and U.S. Steel's output is by assumption a residual after subtracting fringe output from industry demand.

IV. Conclusions

This paper has explained the dynamic relations between market structure and behavior in an industry with a dominant firm and competitive fringe. The dominant price umbrella model was applied to the U.S. steel industry for 1907-1930 and tested through a time-series specification. The dominant firm was found to set its price in re- sponse to the fringe's market share, while the fringe's market share was determined by the dominant firm's price through its effects on both long- run capacity and short-run output decisions by the competitive fringe. These statistical findings thus provide support for the hypothesis that during the years 1907-30, U.S. Steel behaved as a dominant firm.

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dominant firm pricing and fringe expansion: the case of the u.s. iron and steel industry, 1907-1930

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